code: def _indicators(A, b, c, c0, x, y, z, tau, kappa):
      """
      Implementation of several equations from [4] used as indicators of
      the status of optimization.
  
      References
      ----------
      .. [4] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point
             optimizer for linear programming: an implementation of the
             homogeneous algorithm." High performance optimization. Springer US,
             2000. 197-232.
  
      """
  
      # residuals for termination are relative to initial values
      x0, y0, z0, tau0, kappa0 = _get_blind_start(A.shape)
  
      # See [4], Section 4 - The Homogeneous Algorithm, Equation 8.8
      def r_p(x, tau):
          return b * tau - A.dot(x)
  
      def r_d(y, z, tau):
          return c * tau - A.T.dot(y) - z
  
      def r_g(x, y, kappa):
          return kappa + c.dot(x) - b.dot(y)
  
      # np.dot unpacks if they are arrays of size one
      def mu(x, tau, z, kappa):
          return (x.dot(z) + np.dot(tau, kappa)) / (len(x) + 1)
  
      obj = c.dot(x / tau) + c0
  
      def norm(a):
          return np.linalg.norm(a)
  
      # See [4], Section 4.5 - The Stopping Criteria
      r_p0 = r_p(x0, tau0)
      r_d0 = r_d(y0, z0, tau0)
      r_g0 = r_g(x0, y0, kappa0)
      mu_0 = mu(x0, tau0, z0, kappa0)
      rho_A = norm(c.T.dot(x) - b.T.dot(y)) / (tau + norm(b.T.dot(y)))
      rho_p = norm(r_p(x, tau)) / max(1, norm(r_p0))
      rho_d = norm(r_d(y, z, tau)) / max(1, norm(r_d0))
      rho_g = norm(r_g(x, y, kappa)) / max(1, norm(r_g0))
      rho_mu = mu(x, tau, z, kappa) / mu_0
      return rho_p, rho_d, rho_A, rho_g, rho_mu, obj
  
file_path: catboost/contrib/python/scipy/py2/scipy/optimize/_linprog_ip.py
imports: from __future__ import print_function, division, absolute_import
  import numpy
  import scipy
  import scipy.sparse
  from warnings import warn
  from scipy.linalg import LinAlgError
  from .optimize import OptimizeWarning, _check_unknown_options
label_desc: Use image node_id 8 for calling a global function with example usage: _indicators(A, b, c, c0, x, y, z, tau, kappa) and returns: rho_p,  rho_d,  rho_A,  rho_g,  rho_mu,  obj, unknown, unknown, unknown, unknown, np